Understanding Geometric Algebra for Electromagnetic Theory

Provides insight into classical electromagnetic theory through geometric algebra

This practical book promotes the understanding of geometric algebra as a straightforward mathematical toolset for both working with and appreciating the fundamentals of electromagnetic theory. Taking a non-axiomatic, less formal tutorial approach, the text introduces new ideas gradually and goes into considerable detail in giving explanations and working out equations.

After an introduction to geometric algebra, the book shows how to apply it to some basic concepts. Then, the essential toolset is developed, allowing for the application of geometric algebra more generally—for example, in any dimension of space. After applying the toolset to fundamental electromagnetics in the usual (3+1)D situation where space and time are separate entities, the book prepares the ground for a full 4D treatment in which they are treated equally as spacetime vectors. Through geometric algebra, the reader will discover how to tackle the electromagnetic theory of moving charges in a systematic yet uncomplicated way.

In later chapters, the book provides a self-contained primer on the spacetime approach that seeks to avoid the usual conceptual difficulties of special relativity. While this involves some intriguing subtleties, its application is straightforward and readers will see how the toolset unifies previously separate ideas under a single theme: Coulomb's Law + Spacetime = Σ Classical Electromagnetic Theory. The electromagnetic field of an accelerating charge is worked through in detail to show how the toolset is applied.

Most chapters include exercises. There are figures and tables with detailed captions as well as various appendices that offer explanatory information and background material. In particular, a glossary provides an at-a-glance explanation of key terms and symbols.

This book will benefit scientists and engineers who use electromagnetic theory in the course of their work, including those who teach the subject; graduate students and senior undergraduates studying electromagnetics; and electromagnetic theorists.

Problems and solutions materials are available by sending an email to pressbooks@ieee.org